def generatePolydivisibles( _base ):
base = int( _base )
result = list( range( 1, base ) )
newItems = list( range( 1, base ) )
for i in newItems:
yield i
while newItems:
newCandidates = [ ]
while newItems:
item = newItems.pop( 0 )
digits = splitNumber( item, base )
place = len( digits ) + 1
if place % base == 0:
newDigits = [ 0 ]
elif base > 2 and isDivisible( base, 2 ):
if place % ( base / 2 ) == 0:
newDigits = [ 0, base / 2 ]
elif place % 2 == 0:
newDigits = list( range( 0, base, 2 ) )
else:
newDigits = list( range( 0, base ) )
else:
newDigits = list( range( 0, base ) )
newCandidateBase = fmul( item, base )
for digit in newDigits:
testMe = fadd( newCandidateBase, digit )
if isDivisible( testMe, place ):
newCandidates.append( testMe )
yield testMe
newItems = newCandidates
newCandidates = [ ]
def isPolydivisible( n ):
if real_int( n ) < 0:
raise ValueError( 'non-negative, real integer expected' )
strValue = getMPFIntegerAsString( n )
# a couple of cheats
if ( len( strValue ) > 4 ) and ( strValue[ 4 ] not in [ '5', '0' ] ):
return 0
if ( len( strValue ) > 9 ) and ( strValue[ 9 ] != '0' ):
return 0
for i in range( len( strValue ), 1, -1 ):
current = mpmathify( strValue[ : i ] )
if not isDivisible( current, i ):
return 0
return 1
def isHarshadNumber( n, k ):
digits = getBaseNDigits( real_int( n ), k )
return 1 if isDivisible( n, fsum( digits ) ) else 0
